Topics in Synchronization and Motion Control
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This thesis considers three issues: the problem of output synchronization in homogenous and heterogeneous networks of linear agents, the problem of path following for 3-DOF marine vehicles, and the problem of motion control of marine craft using the concepts from analytical mechanics. The thesis studies synchronization of multi-agent systems in the presence of external disturbances, and brings forth the notions of "H∞ almost synchronization", "H∞ almost regulated synchronization", and "H∞ almost formation". In almost synchronization, the objective is to nd decentralized, distributed, dynamic protocols so that agents reach an agreement on a certain quantity of interest with any arbitrary degree of accuracy, which should be de ned appropriately. The objective of the "H∞ almost" synchronization problem is to find protocols such that the H∞-norm of the transfer function from disturbance to synchronization errors can be made arbitrarily small. Similarly, the problem of H1 almost regulated synchronization with respect to a reference, which is generated by an exosystem and is known to a subset of agents, is to nd protocols such that the H∞-norm of the transfer function from disturbance to regulation errors can be made arbitrarily small; thus, any arbitrary degree of accuracy can be obtained for regulation. The thesis considers multi-agent systems in which communication links are unidirectional. Agents are assumed to have multiple inputs and multiple outputs, and are described by linear, time-invariant models. The problem of H∞ almost synchronization is rst solved for heterogeneous networks of introspective agents; i.e. networks possess nonidentical agents which have access to their own output. From a practical point of view, both local and global sensing are required for such networks. Moreover, the problem of H∞ almost synchronization is solved for homogeneous networks of non-introspective agents; i.e. networks possess identical agents which have no access to their own state or output. Therefore, only local sensing is essential. The protocols are derived based on the structural properties of agents. The design procedures are given in a step-by-step manner, and the proofs are provided in details to reveal the strong mathematical features of the methodology. In addition, the thesis conducts a study of path-following control methods for 3-DOF marine craft. Innovative results are presented for straightline path-following in which a particular emphasis is forwarded to the role of speed. Two approaches are proposed so that the speed becomes dynamically dependent on the geometric error and its derivative. In one approach, backstepping is utilized, and a nonlinear dynamic controller is derived. Under the proposed control law, the vehicle accelerates during transient to move toward the path with higher speeds than the desired speed. In the other method, with the aid of the method of least squares, a nonlinear controller for path following is derived. The controller is rst designed for fully actuated craft, and then applied to a linearized model of underactuated vessels. It provides a less-computationally extensive method to deal with external disturbances by inclusion of an integral action to the system. In fact, it allows the marine craft to compensate for external forces by increasing the speed. This approach lends itself to cooperative path following. Moreover, the thesis presents a framework for motion control of marine craft using [the accepted principles of] analytical mechanics. More accurately, a motion control problem is portrayed as the modeling problem of a constrained multi-body system, and the Lagrangian approach to nd the equation of motion of constrained systems is taken into consideration in order to nd the forces under which the system moves in a way that the constraints are satis ed exactly. These forces are considered as the control forces, and are applied to the system by virtue of the actuators. Therefore, the system is controlled as if Nature has been the control engineer. The novelty of the work is to generalize a recently established framework to incorporate both holonomic and nonholonomic constraints; thus, scenarios such as path maneuvering or coordinated path following fall within the scope of the framework. A leader-follower formation is given as an illustration.